Question

A brewer is trying to maximize the alcohol content of his new
Stout. He experiments by varying the amount of grain added to each
batch, with 3 different weights: 1 pound, 1.25 pounds, and 1.5
pounds. He run 5 replicates of each batch, and gets the following
results:

1.0 lbs 1.25 lbs 1.5 lbs

5.12 5.11 6.03

5.34 5.53 5.58

5.17 4.18 5.74

4.58 5.45 6.19

5.10 4.69 6.06

What is the hypothesis the brewer is testing in this
experiment?

Null Hypothesis

What are the 2 assumptions he must verify before proceeding?

What is your analysis of the impact of grain added to alcohol
content at =0.05?

Answer #1

Here we will use one way anova

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha: At least one mean is different.

where is mean for 1 pounds

is mean for 1.25 pounds

is mean for 1.5 pounds

The 2 assumptions he must verify before proceeding are

All populations have a common variance and all samples are drawn independently of each other.

Now by using SPSS i'm analysing the data

Here factors are for 0-1 pounds

1-1.25 pounds

2-1.5 pounds.

Here test statistic is

F= MS(Between groups)/M.S(Within groups)

F= 1.335/0.154

F=8.697

P VALUE= 0.005 WHICH IS SMALLER THAN 0.05 LEVEL OF SIGNIFICANCE HENCE SIGNIFICANT.

CONCLUSION: **SINCE P VALUE IS SIGNIFICANT WE REJECT NULL
HYPOTHESIS H0 AND CONCLUDE THAT AT LEAST ONE MEAN IMPACT OF GRAIN
ADDED TO ALCOHOL IS DIFFERENT.**

I DID ABOVE TUKEYS TEST

(1.25 POUNDS VS 1.0 POUNDS) IS SIGNIFICANT P= 0.012

(1.25 POUNDS VS 1.5 POUNDS) IS SIGNIFICANT P=0.07

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